Previous electrophoretic transport experiments with zwitterionic lipid vesicles revealed that the regulation of the solution pH via buffer addition reduces the anionic surface charge strength of dipolar membranes [1]}. The consequence of this protonation effect on membrane interactions is qualitatively characterized in Fig. REF (c). One sees that upon the reduction of \(Q_-\) , the attractive interaction regime is suppressed, and the net pressure becomes more repulsive. The enhancement of the membrane repulsion by the reduction of \(Q_-\)  stems from the increase of the effective dipolar charge in Eq. (REF ), and the amplification of the repulsive force component in Eq. (REF ), i.e. \(Q_-\downarrow Q_{\rm eff}\uparrow P\uparrow \) . Taylor-expanding now Eq. (REF ) for \(Q_{\rm eff}/Q_+\lesssim 1\) , one obtains
\(d^*\approx 2(p+a)-2a\frac{|Q_{\rm eff}|}{Q_+}\frac{\cosh (\kappa _{\rm s}p)}{\sinh \left[\kappa _{\rm s}(p+a)\right]}.\) 
